10t^5-2t^3-4t^4=

Solution for 10t^5-2t^3-4t^4= equation:

Simplifying
10t5 + -2t3 + -4t4 = 0

Reorder the terms:
-2t3 + -4t4 + 10t5 = 0

Solving
-2t3 + -4t4 + 10t5 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2t3'.
2t3(-1 + -2t + 5t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 't3' equal to zero and attempt to solve:

Simplifying
t3 = 0

Solving
t3 = 0

Move all terms containing t to the left, all other terms to the right.

Simplifying
t3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-1 + -2t + 5t2)' equal to zero and attempt to solve:

Simplifying
-1 + -2t + 5t2 = 0

Solving
-1 + -2t + 5t2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-0.2 + -0.4t + t2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -0.4t + 0.2 + t2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -0.4t + t2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -0.4t + t2 = 0 + 0.2
-0.4t + t2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-0.4t + t2 = 0.2

The t term is -0.4t.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4t + 0.04 + t2 = 0.2 + 0.04

Reorder the terms:
0.04 + -0.4t + t2 = 0.2 + 0.04

Combine like terms: 0.2 + 0.04 = 0.24
0.04 + -0.4t + t2 = 0.24

Factor a perfect square on the left side:
(t + -0.2)(t + -0.2) = 0.24

Calculate the square root of the right side: 0.489897949

Break this problem into two subproblems by setting 
(t + -0.2) equal to 0.489897949 and -0.489897949.

Subproblem 1
t + -0.2 = 0.489897949

Simplifying
t + -0.2 = 0.489897949

Reorder the terms:
-0.2 + t = 0.489897949

Solving
-0.2 + t = 0.489897949

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '0.2' to each side of the equation.
-0.2 + 0.2 + t = 0.489897949 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + t = 0.489897949 + 0.2
t = 0.489897949 + 0.2

Combine like terms: 0.489897949 + 0.2 = 0.689897949
t = 0.689897949

Simplifying
t = 0.689897949

Subproblem 2
t + -0.2 = -0.489897949

Simplifying
t + -0.2 = -0.489897949

Reorder the terms:
-0.2 + t = -0.489897949

Solving
-0.2 + t = -0.489897949

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '0.2' to each side of the equation.
-0.2 + 0.2 + t = -0.489897949 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + t = -0.489897949 + 0.2
t = -0.489897949 + 0.2

Combine like terms: -0.489897949 + 0.2 = -0.289897949
t = -0.289897949

Simplifying
t = -0.289897949

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.689897949, -0.289897949}
Solution
t = {0.689897949, -0.289897949}